The present invention relates to a method and apparatus for reconstruction of a multi-dimensional image. In particular, the present invention is directed to image reconstruction of a bi-dimensional or three-dimensional image of an object, for example part of the body of a patient, from a set of projections respectively mono-dimensional or bi-dimensional of this object, obtained for different positions of apparatus for viewing around the object. The invention particularly relates to medical imagery by tomographic reconstruction.
Tomography produces images of slices of an object by acquiring measurements integrated along lines, a measure of a physical parameter of the object using a detector that revolves around the object over at least 180° (with additional treatment more restricted angular ranges can be adopted). The slices are reconstructed by calculation typically as planes orthogonal to the axis of rotation (oscillations of the axis of rotation from one angle of projection to the other are tolerated).
The result is an image of the distribution of the physical characteristic of this object, a characteristic such as the attenuation coefficient for tomography calculated from X-rays and CT imaging, or such as radioactivity for emission tomography, or such as trajectories found in rotational angiography.
Such reconstruction operations utilize substantial computer processing, especially in the form of projections (transformations from a dimension space d to a dimension space d-1) and in the form of filter- or back-projections (transformation from a dimension space d-1 to a dimension space d),
Three types of reconstruction are known, which correspond to three different acquisition geometries. Reconstruction geometry defines the relation between a source of a measuring line forming the object of an integral, with a set of measuring points. In a first geometry, known as parallel-beam geometry, the source is considered as being at an infinite distance from the detector and all the measuring lines have the same direction, given by the angle of projection. In a second geometry, known as fan-beam geometry, the source is at a finite distance from the detector, called a focal distance and all the measuring lines define a fan diverging in a plane, a plane intercepted by a linear detector. The direction of the optical axis is defined by the line which is orthogonal to the detector and which passes through the source. This direction is defined by the angle of projection. A third geometry, known as cone-beam geometry, is a generalisation of the fan-beam geometry, in which the measuring lines define a cone in three dimensions, a cone departing from the source and intercepted by a detector in two dimensions, that is, by a detection surface.
In these three geometries, tomographic reconstruction requires heavy calculation, e.g., computer-intensive mapping, to transform the set of measurements made at different angles (oblique measurements) in reconstructed data which have to be calculated in a set of reconstruction points distributed in a predetermined manner on the object to be reconstructed. This problem of the importance of the calculation is also posed when it is a question of moving from an interim reconstructed object to projections of this reconstruction on virtual oblique detector positions, particularly in the scope of reconstructions by iteration which imply a succession of such projections then reconstructions with comparison of the virtual projections and the real projections at each iteration.
Within the scope of the geometry cone-beam geometry, the slices are not generally constructed from independent sinograms, but are reconstructed from the same set of surfaces of surface measurements. The reconstruction is considered 3D and the cost in calculating between the volume reconstructed in 3D and the surface measurements is even higher.
To rectify this problem, a known method comprises re-sampling the reconstructed object to align the set of reconstruction points successively with each successive direction of oblique detector. All the same, the re-sampling at each angle of projection is an equally costly in calculation.
Within the scope of projection with parallel-beam geometry, a technique for facilitating the task of treatment is also known as will be described with respect to FIG. 1.